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19 February 2006

how to play a nice casual spontaneous game of FischerRandom Chess in the park without batteries

Figure 1. Dice for Hoon Craps

Vleeptron Scavenger Hunt
No. 1

Find where to buy
a set of Platonic Dice
on the Web.

The first instinct to determine how to set up a game of FischerRandom Chess is to program a computer and use its Random Number Generator.

On the other hand, if you don't need to lug around a computer to play Ordinary Chess, why shouldn't FischerRandom Chess be just as portable? And what good is a fancy FRC handheld if you can't begin to play if the battery's dead? The next thing that will happen is that you'll take the battery out of the smoke detector, forget to put it back, and die in a ghastly fire.

FRC can be just as portable as Ordinary Chess. It can be entirely manual.

Okay, first you need a set of verkakte Platonic Dice (see Figure 1). They are the 5 Platonic Solids:

...........regular faces with
...........numbers from
solid......1 to
==============================
tetrahedron.....4
cube............6
octahedron......8
dodecahedron...12
icosahedron....20

They are called Platonic Solids because they were probably discovered by Pythagoras and discussed by Euclid. Plato thought these guys were absolutely brilliant and said so often. He himself never invented anything original in mathematics.

In ordinary everyday Cartesian xyz Space, there exist five regular solids -- a solid where all faces are the same size and shape, and all the angles the faces make with each other are the same angles. The cube is one of them, so is the tetrahedron. The Great Pyramid at Giza
has a square bottom and four triangle faces, so it's neither a tetrahedron nor a regular Platonic solid.

One of the classic unsolved mathematics questions of the Ancient Greeks was "doubling the cube." Given one cube, how long must an edge of a second cube be so it has twice the volume of the first cube? Evariste Galois, a 20-year-old French guy, solved that the night before he fought a pistol duel in 1832 over a woman named
Stephanie-Felice du Motel, and then died a few days later.

In the margin as he dashed out the manuscript of all he had discovered in mathematics, he scribbled: There is no time.

If you enjoy playing Hoon Craps, you probably already have these dice around the house. I have no idea where to buy these on Earth. If you know where to buy Platonic Dice, Leave A Comment.

How much should a set of Platonic Dice cost? What's fair?

This method produces each of the 960 starting positions in FRC with equal probability.

If one has polyhedral dice shaped like each of the Platonic solids, one never needs to reroll any dice.

[For some mysterious reason, this reminds me of a game called TAGWOR.]

* Roll the dice.

* Place a white bishop on the square indicated by the octahedron.

* Place the other white bishop on the square of opposite colour indicated by the tetrahedron.

* Place the white queen on the square indicated by the cube.

* Take the number of the icosahedron.

* Subtract one.

* Divide by four.

* Add one to quotient and remainder. These determine positions of the first and second knight.

* Place the white rooks and the white king between the rooks. If desired, use the dodecahedron to decide who plays white (even numbers for one player, odd for the other).

* Place the white pawns and mirror the position for black.

2 Comments:

Anonymous Jim Olson said...

Um, I own a set of platonic dice.

Anyone who played Dungeons and Dragons in the 80's owns a set...they were essential to play.

I've become fascinated with Go. I don't particularly like board games. Chess escapes me, I can't think that far ahead and I don't really know anyone who plays. (I'm sure I could find a chess club to go to.)

But Darrick LOVES board games. So, I am going to buy an inexpensive Go board for him for his birthday. Neither of us know how to play, but he is very quick with rules.

21:33  
Blogger Bob Merkin said...

The rules are really easy, much easier than chess.

Playing well -- that's a lifetime's commitment.

Still today, anyone with ambitions to be a great competitive Go master commonly goes to live with the family of a master to learn the highest levels of the game. I know a math professor who lived with a Go master in Japan for a year.

Immigrants from Southeast Asia in the last 25 years have given American Go a huge booster shot in the dupa. Suddenly in many large cities it's easy to find a Go club crawling with top-level players.

But I still think the oddest thing about Go is how chess fell to the computers, but Go is still hugely resistant to the best efforts of Our Silicon Pals. With MIT, Boston should be a hotbed of the Computer Go subculture. Big Artificial Intelligence conventions regularly have a Computer Go competition sideshow. First 20 good programs compete -- and then typically some 12-year-old kid wipes the floor with the computer program champ.

And yet the rules of Go are so much simpler than chess. On any intersection, either there's nothing, or a white stone, or a black stone. There's no element of luck or chance (as in backgammon).

Learners use boards smaller than 19 x 19, good models to learn the elements of play.

01:54  

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